# Questions tagged [philosophy-of-mathematics]

Philosophy of mathematics asks questions about mathematical theories and practices. It can include questions about the nature or reality of numbers, the ground and limits of formal systems and the nature of the different mathematical disciplines.

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### When does “zero” exist?

When does zero exist? ex: if i say, "I dont have a hat" it seems more fair to say -1(hat) rather than 0(hat) ,because 0(hat)=0 would mean (hat)=0 and -1(hat)=(-hat) implying there is a hat in ...
210 views

### An abstract problem in philosophy of language [closed]

Suppose H and P swim in the river on days A and B. Ask H and P Did you swim in the river twice? P says yes, on day A of river A (with condition A) and day B (with condition B). But H says no, I did ...
84 views

### A question about proof [closed]

I read the book of geometry (Euclid) almost simultaneously with Plato's Republic. For a long time, the question remained: why did Plato's speech in the Republic, and of course his other books, did ...
141 views

### Can True(X) be completely defined as Provable(X) for some X? [closed]

This following seems to provide a concrete example that fulfills my updated question: This defined subset of finite strings only specify the arithmetic operation of addition "+" and the Boolean ...
198 views

### Comparisons between two notions of existence

I have the following, rather naive question: To what extent can the a priori existence of mathematical objects be reasonably compared with the seemingly a posteriori existence of objects established ...
371 views

### Why was the zero not discovered long ago or in the beginning? [closed]

The rules governing the use of zero appeared for the first time in Brahmagupta's Brahmasputha Siddhanta (7th century). This work considers not only zero, but also negative numbers and the algebraic ...
122 views

### Language is countable while (sunsets of)natural number is uncountable? [closed]

Of course "natural number" can be seen as the common feature in countless implementations(such as Sn={n}∪n and Sn={n},as natural number is just isomorphic to the sets*. But the the "natural number" is ...
531 views

### Is mathematics forced upon us or arbitrary?

Math at its core begins with calling something true or false and following logic. WE for example call an odd number 2n+1, but what if we called an odd number 2n and flipped it for it to become an even ...
58 views

### Could math be different? [duplicate]

I ask this philosophical question out of curiosity. Is math in its "best" form? Since math was first created, of counting numbers 1,2,3 etc... I wonder is this the best way to count? Can our brains we ...
148 views

### Human Mind vs Computer

We start from axioms, use rules of logic, and derive theorems. These theorems establish what is the case in relation to the context. In all disciplines employing mathematics, we reason by saying '...
65 views

### Could Heraclitus use the word “river”? [closed]

Could Heraclitus use the word "river"? (This is still a question) If you look very closely, at the highest level of accuracy, no experience is repeated twice. This is reminiscent of the phrase ...
259 views

### Is Mathematics the Ultimate Culmination of Analytic Philosophy?

As a novice amateur, the similarities between mathematics and analytic philosophy seem striking to me. At least in a caricature view of analytic philosophy, it is the project of establishing the ...
224 views

### Are there recent coherence theory of truth for mathematical truths?

Are there any recent works (papers, books, etc) in philosophy of mathematics where it is given an account of mathematical truth in terms of a coherence theory of mathematical truth? I am interested ...
76 views

### The limit of mathematics [closed]

Does mathematics have a limit? Could we at one point say that we don't have anything left to discover? If yes, would it mean that ours is perfect civilization?
726 views

### Was Kant a factor in forming Gauss's abstract view of mathematical objects?

Gauss argued for philosophical issues important to the development of mathematics, such as the identity of complex numbers, among others. I wonder what philosophical currents influenced his thinking ...
2k views

### Can there be a universe with different mathematics?

I do not know what exactly I mean by other universes, but I just have a feeling that mathematics is somehow inevitable. For example the law of "excluded middle" (LEM). If there are aliens, can we ...
394 views

### can we reason about logic?

People who study mathematical logic make arguments about logic itself. So it seems that people take for granted an "intuitive logic" (otherwise, how would they form arguments?). So the observation is ...
245 views

### Hilbert's formalism and game formalism differences and similarities

I've recently encountered differences between Hilbert's formalism and game formalism. They seem pretty much similar in my eyes. I wish to understand in what way does Hilbert’s formalism resemble game ...
245 views

### Another critique of the unreasonable effectiveness of mathematics in natural sciences

It seems the majority of scientists hold for a the hyper-effectiveness of mathematics in natural sciences as a sign that nature is deeply mathematical. Although I believe that some mathematisism is ...
665 views

### Are there two different mathematics in philosophy?

I was looking at arguments about mathematics being a science (or not), here for example, but it seems that these arguments are more about some metaphysical idea of mathematics rather than the subject ...
214 views

### Can we imagine a perfect circle?

Applied mathematicians often work with circles, but I'm guessing it's an abstraction that cannot save all the empirical data. Can we conceive of a perfect circle in our visual field -- as apparently ...
101 views

### Does Tegmark himself include paraconsistent mathematical structures in his mathematical multiverse hypothesis?

Tegmark postulates in his hypothesis that all possible mathematical structures would exist. But does he include also possible mathematical structures described by other types of logic like ...
187 views

### When is it meaningful to say that an undecided conjecture is true or false?

I see that other questions have already been asked about mathematical truth but here I want to ask clarifications on a particular perspective. One can think the answer to the question could be "when ...
27 views

### What are the possible philosophical inspirations for the philosophical concept of “antifragility” that was defined by Taleb?

It seems to me that this is just a generalization of "hormesis" by trivially abstracting some of it's aspects but I am not very well versed in philosophy.
296 views

### Does God need to create mathematics?

If someone knows the detail of everything and has endless life, did s/he need to create mathematics to describe the world?
262 views

### Can anything be less than one?

Zero itself seems to be an absurd number because if there is really zero of something, then nobody has ever sensed it. But even with temperatures, we don’t really have negative and positive ...
89 views

### Are mathematical axioms arbitrary?

I've been thinking recently about whether or not mathematical axioms are arbitrary. I'm trying to figure out what axioms in systems are derived from and just how arbitrary they really are. My main ...
59 views

### What is the meaning of Principle C'' in Hartry Field's 'Science Without Numbers'?

For Field, the following is 'perfectly obvious', but I would like confirmation that I understand it completely. Let A be a nominalistically statable assertion. Let A* be the assertion that results by ...
211 views

### (Non-)Mathematical examples - towards a philosophy of mathematics-

I need your help: I'm looking for a list of interesting examples (see below) that are of high interest to philosophy of mathematics. To specify this, I need you to consider the following: ''...
200 views

### How do philosophers formally characterise mathematical objects?

In the Stanford Encyclopedia of Philosophy article 'Platonism in the Philosophy of Mathematics' the following formalisation is given for the existence of a mathematical object: "Existence can be ...
174 views

### Why does Gödel's incompleteness theorem apply to multiple formal systems?

Any consistent formal system F within which a certain amount of elementary arithmetic can be carried out is incomplete; i.e., there are statements of the language of F which can neither be proved nor ...
6k views

### Isn't the notion that everything will occur in an infinite timeline an example of the gambler's fallacy?

I've seen a few different formulations of this, but the most famous is "monkeys on a typewriter" - that if you put a team of monkeys on a typewriter, given infinite time, they will eventually produce ...
51 views

### Does Weyl's tile argument defeat the discrete spacetime?

Weyl shows that in a discrete spacetime Pythagoras's theorem fails to arise. Of course it may be that although Pythagoras's theorem arises naturally but actually does not model the real world. So Does ...
262 views

### Mathematical models of dynamic algorithmic processes

This question primarily concerns dynamical or time-dependent phenomena in philosophy and to what extent such heuristic discourse features in more precise mathematical settings. In order to model ...
96 views

### Hume on infinity

I know Hume argued against dividing finite space into infinitely many regions, but I can't seem to find anything regarding his thoughts on infinity itself. From his Enquiry you sort of get that he ...
94 views

### In non-platonism, can undecidable statements have truth value?

Most sources I can find about Gödel's incompleteness theorems summarize the result as "there exist true arithmetical statements that have no proof." It seems coherent to say that there exist ...
3k views

### Why does Wittgenstein have a problem with writing “f(a, b). a = b"?

Why does Wittgenstein have a problem with logical statements saying nothing ? (5.5303) . How would Wittgenstein want us to interpret f(a,a) ? He also mentions axiom of infinity from which Russell ...
49 views

### If intuitionism were true, could a mathematical system exist that is incompatible to our system?

If mathematical intuitionism were true, could there be a System that Describes reality accurately and consistently like current maths do Consists of equations that cannot be described by current ...
59 views

### About Wigner's view on the relation between mathematics and physics?

Physicist Eugene Wigner argued that the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious and that there is no rational explanation for it ...
351 views

### What is the relevance of applicability to the natural sciences in pure mathematics?

I think I am coming to a good, new understanding of the relationship of pure mathematics to the natural sciences. A major concern of mine is just how reliable is rigorous (characteristically "pure") ...
135 views

### Does the finitary proof of the consistency of relevant PA shows that first order PA is irrelevant?

Relevance logic takes a closer look at the implication operation in first-order logic. It suggests that implications such as: p and not p -> q cannot hold; in ordinary English, an example of this ...
190 views

### The notion of knowledge for Kant and mathematical objects

As far as I understand the notion of knowledge in Kantian philosophy, we cannot speak of knowing something unless there is a relation between its concept and some object of intuition in experience. ...
361 views

### Are mathematical suppositions of physical theories determined uniquely according to Aristotle and Plato?

Does mathematics apply to physics in one way or multiple ways? What do Aristotle and Plato think? It would seem that Aristotle thinks mathematics can be applied to physics in one way only because, ...
121 views

### How do you resolve the issue: logically reasoning about 'god' (or even physics; mathematics) when sometimes logic is not valid or is partially broken?

Granted, the start of the following discussion may use some common everyday common sense logic, and therefore may not be valid in some new paradigm. However, the question is, in the face of Russel's ...
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### What do we mean by the symbolic representation of nothing?

The word 'nothing' symbolically represents nothing-in-itself. But how can we refer to something that by definition is not there? To make this clearer: the word 'horse' refers to an actual living ...
322 views

### Was Gödel the first person to bring up that truth always exceeds the grasp of proof?

Was Gödel the first person to pose and solve this question in mathematics? In the larger philosophical debate, has this question been posed before? Say by Plato or Aristotle? One could interpret for ...
397 views

### Can infinity be made finite in certain conditions?

In mathematics there are not only infinitely big numbers, but also infinitely small numbers. One can consider arbitrarily small numbers that can exist only in the mathematical world. For example, ten ...
78 views

### what is the ontology-ideology distinction in phil of math

Quine proposed a distinction between ontology - the doctrine of what there is - and ideology - the complex terms and predicates expressible in one's theoretical language (though in his 1971 paper he ...